Question

Volumes of two cylinders of radii $R$, $\frac{R}{2}$ and heights $H,h$ respectively are equal. Then $H:h=$ ___

• A. $1:2$
• B. $1:4$
• C. $2:1$
• D. $4:1$

Answer 1

The correct option is B $1:4$

Volume of a cylinder of Radius $R$ and height $H=\pi R^{2}H$
So, volume of a cylinder of radius $\frac{R}{2}$ and height $h=\pi {\left(\frac{R}{2}\right)}^{2}h=\frac{\pi R^{2}h}{4}$
Given , these volumes are equal.
So, $\pi R^{2}H=\frac{\pi R^{2}h}{4}$
$\Rightarrow H=\frac{h}{4}$
$\Rightarrow H:h=1:4$